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Research Papers: Design Automation

A Random Process Metamodel Approach for Time-Dependent Reliability

[+] Author and Article Information
Dorin Drignei, Ervisa Kosova

Mathematics and Statistics Department,
Oakland University,
2200 N. Squirrel Road,
Rochester, MI 48309

Igor Baseski, Zissimos P. Mourelatos

Mechanical Engineering Department,
Oakland University,
2200 N. Squirrel Road,
Rochester, MI 48309

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received December 31, 2014; final manuscript received October 10, 2015; published online November 16, 2015. Assoc. Editor: Nam H. Kim.

J. Mech. Des 138(1), 011403 (Nov 16, 2015) (9 pages) Paper No: MD-14-1846; doi: 10.1115/1.4031903 History: Received December 31, 2014; Revised October 10, 2015

A new metamodeling approach is proposed to characterize the output (response) random process of a dynamic system with random variables, excited by input random processes. The metamodel is then used to efficiently estimate the time-dependent reliability. The input random processes are decomposed using principal components, and a few simulations are used to estimate the distributions of the decomposition coefficients. A similar decomposition is performed on the output random process. A Kriging model is then built between the input and output decomposition coefficients and is used subsequently to quantify the output random process. The innovation of our approach is that the system input is not deterministic but random. We establish, therefore, a surrogate model between the input and output random processes. To achieve this goal, we use an integral expression of the total probability theorem to estimate the marginal distribution of the output decomposition coefficients. The integral is efficiently estimated using a Monte Carlo (MC) approach which simulates from a mixture of sampling distributions with equal mixing probabilities. The quantified output random process is finally used to estimate the time-dependent probability of failure. The proposed method is illustrated with a corroding beam example.

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Figures

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Fig. 1

Corroded beam under bending [2]

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Fig. 2

A sample of 50 random input functions F(t) (upper left); principal component reconstruction using r = 6 (lower left); corresponding 50 random output functions G(t) (upper right); principal component reconstruction using s = 4 (lower right)

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Fig. 3

Eigenvalue cumulative contribution of variance, for input (left) and output (right) processes

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Fig. 4

Scatter plots of the six components of input vector α

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Fig. 5

Scatter plots of the four components of output vector δ

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Fig. 6

Time-dependent probability of failure based on direct MC simulation (solid), new metamodel (dashed), and standard metamodel with bounded domain (dotted with circle markers)

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